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Fine properties of minimizers of mechanical Lagrangians with Sobolev potentials

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  • In this paper we study the properties of curves minimizing mechanical Lagrangianwhere the potential is Sobolev. Since a Sobolev functionis only defined almost everywhere, no pointwise results can be obtained in this framework,and our point of view is shifted from single curves to measures in the space of paths.This study is motived by the goal of understanding the properties ofvariational solutions to the incompressible Euler equations.
    Mathematics Subject Classification: Primary: 49Kxx, 49Lxx; Secondary: 70H03, 37J50.


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